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Automatic Quadratic Factorization
Enter a quadratic polynomial in the form ax² + bx + c and get the factored result automatically. See results instantly without complex calculations.
Polynomial Factorization Calculator
Enter a quadratic polynomial ax² + bx + c to see its factored form.
Result
Original
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Discriminant (D)
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Factored
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Roots
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Learn more
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Check Factorizability with Discriminant
Calculate discriminant D = b² - 4ac to check if factorization is possible and the type of roots. D > 0 gives two distinct real roots, D = 0 gives a double root, D < 0 gives complex roots.
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Math Learning and Problem Solving
Quickly check answers to factorization problems taught in middle and high school math classes and understand the calculation process.
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Using the Quadratic Formula
Use the quadratic formula x = (-b ± √D) / 2a to calculate exact roots and derive the factored form based on them.
Frequently asked questions
What is the discriminant (D) and why does it matter?
The discriminant is D = b² - 4ac, and it tells you the type of roots before solving. D > 0 gives two distinct real roots, D = 0 gives a repeated (double) root, and D < 0 gives complex roots that cannot be factored over the reals.
If D is negative, does that mean it cannot be factored at all?
It cannot be factored using real numbers. It can still be factored using complex roots, and this calculator will show "No real roots (complex)" in that case.
Can I enter decimals or negative numbers for a, b, and c?
Yes. All three coefficients accept real numbers, including decimals and negative values. The only requirement is that a cannot be zero, since that would no longer be a quadratic equation.
How does the factored form relate to the roots?
For ax² + bx + c with roots r1 and r2, the factored form is a(x - r1)(x - r2). Plugging the roots found via the quadratic formula directly into this expression gives the factored result.
Can this calculator factor cubic polynomials too?
Yes, in addition to the quadratic tab, this calculator also provides a cubic tab for factoring higher-degree polynomials.